Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

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Oblique Shock

Expansion Waves

✖Density Ahead of Oblique Shock refers to the air or fluid density before encountering an oblique shock wave.ⓘ Density Ahead of Oblique Shock [ρ₁]			+10% -10%
✖The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Oblique Shock [γ_o]			+10% -10%
✖Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.ⓘ Upstream Mach Normal to Oblique Shock [M_n1]			+10% -10%

✖Density Behind Oblique Shock signifies the air or fluid density after passing through an oblique shock wave.ⓘ Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number [ρ₂]

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Formula

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Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number

Formula

`"ρ"_{"2"} = "ρ"_{"1"}*(("γ"_{"o"}+1)*("M"_{"n1"}^2)/(2+("γ"_{"o"}-1)*"M"_{"n1"}^2))`

Example

`"2.501226kg/m³"="1.225kg/m³"*(("1.4"+1)*(("1.606")^2)/(2+("1.4"-1)*("1.606")^2))`

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Download Oblique Shock and Expansion Waves Formulas PDF

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))
ρ₂ = ρ₁*((γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2))
This formula uses 4 Variables

Variables Used

Density Behind Oblique Shock - (Measured in Kilogram per Cubic Meter) - Density Behind Oblique Shock signifies the air or fluid density after passing through an oblique shock wave.
Density Ahead of Oblique Shock - (Measured in Kilogram per Cubic Meter) - Density Ahead of Oblique Shock refers to the air or fluid density before encountering an oblique shock wave.
Specific Heat Ratio Oblique Shock - The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Upstream Mach Normal to Oblique Shock - Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

STEP 1: Convert Input(s) to Base Unit

Density Ahead of Oblique Shock: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Specific Heat Ratio Oblique Shock: 1.4 --> No Conversion Required
Upstream Mach Normal to Oblique Shock: 1.606 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ₂ = ρ₁*((γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2)) --> 1.225*((1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2))

Evaluating ... ...

ρ₂ = 2.50122632413082

STEP 3: Convert Result to Output's Unit

2.50122632413082 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

2.50122632413082 ≈ 2.501226 Kilogram per Cubic Meter <-- Density Behind Oblique Shock

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Oblique Shock » Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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< 10+ Oblique Shock Calculators

Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number

Go Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)))

Flow Deflection Angle due to Oblique Shock

Go Flow Deflection Angle Oblique Shock = atan((2*cot(Oblique Shock Angle)*((Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle))^2-1))/(Mach Number Ahead of Oblique Shock^2*(Specific Heat Ratio Oblique Shock+cos(2*Oblique Shock Angle))+2))

Temperature Ratio across Oblique Shock

Go Temperature Ratio Across Oblique Shock = (1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))

Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number

Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1)))

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number

Go Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))

Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number

Go Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))

Density Ratio across Oblique Shock

Go Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)

Component of Downstream Mach Normal to Oblique Shock

Go Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)

Pressure Ratio across Oblique Shock

Go Pressure Ratio Across Oblique Shock = 1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)

Component of Upstream Mach Normal to Oblique Shock

Go Upstream Mach Normal to Oblique Shock = Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle)

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number Formula

Which parameters govern the changes of flow properties across oblique shock?

Oblique shock wave properties in a calorically perfect gas depend only on the normal component of upstream Mach no and which in turn is a function of upstream Mach no. and wave angle. In contrast, the changes in flow properties across normal shock depend on upstream Mach no only.

How to Calculate Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number?

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number calculator uses Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)) to calculate the Density Behind Oblique Shock, The Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number formula describes the density of the fluid immediately behind an oblique shock wave. This formula quantifies how the density of the flow changes behind an oblique shock wave, considering parameters such as the upstream density, Mach number, and shock wave angle. Density Behind Oblique Shock is denoted by ρ₂ symbol.

How to calculate Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number using this online calculator? To use this online calculator for Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number, enter Density Ahead of Oblique Shock (ρ₁), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) and hit the calculate button. Here is how the Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number calculation can be explained with given input values -> 2.501226 = 1.225*((1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2)).

FAQ

What is Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number?

The Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number formula describes the density of the fluid immediately behind an oblique shock wave. This formula quantifies how the density of the flow changes behind an oblique shock wave, considering parameters such as the upstream density, Mach number, and shock wave angle and is represented as ρ₂ = ρ₁*((γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2)) or Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)). Density Ahead of Oblique Shock refers to the air or fluid density before encountering an oblique shock wave, The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

How to calculate Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number?

The Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number formula describes the density of the fluid immediately behind an oblique shock wave. This formula quantifies how the density of the flow changes behind an oblique shock wave, considering parameters such as the upstream density, Mach number, and shock wave angle is calculated using Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)). To calculate Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number, you need Density Ahead of Oblique Shock (ρ₁), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1). With our tool, you need to enter the respective value for Density Ahead of Oblique Shock, Specific Heat Ratio Oblique Shock & Upstream Mach Normal to Oblique Shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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